Approximation with Convolution Operators

摘要

Global results on approximation with convolution operators containing the modulus of continuity of functions involved are summarized. Local results of Voronovskaya-type are recorded including a list of such results for particular operators. The main part of the paper deals with a relation between these two ways of approximation in the sense that under a certain condition from a Voronovskaya-type formula a result follows concerning the best global approximation for the whole class of functions involved and conversely.